(TNS) House Democrats plan to press forward on voting, starting Wednesday, on a series of gun control proposals, most of which appear to have slim chance to become law amid Republican opposition in the evenly divided Senate.

In the wake of a recent wave of mass shootings at a Texas elementary school and across the country, Democrats have largely united on gun violence prevention measures that would raise the age to purchase certain firearms, or back “red flag” laws for emergency gun seizures and other proposals.

If the House passes the bills, they would head to the Senate and await action along with two measures the House passed last year to expand criminal background checks prior to gun purchases.

As Florida Democratic Rep. Debbie Wasserman Schultz put it at a gun victims event Tuesday on the National Mall, the action would be taken “to put pressure on the United States Senate to at least do something.”

But Sen. John Cornyn of Texas, a key Republican in bipartisan negotiations for gun proposals that could make it through the Senate, quashed some of those hopes Monday night when he signaled that Republicans would not accept many of the proposals.

Cornyn said on the Senate floor that he would not back expanded background checks or raising the age to purchase certain rifles — key parts of the House bill. “Targeted reforms, I think, is the way to get to where we need to go,” Cornyn said.

Cornyn said he may back efforts to keep guns out of the hands of criminals or those who have mental health problems. A proposal from Cornyn to expand notifications of background check denials was included in the Violence Against Women Act reauthorization earlier this year.

“What I’m interested in is keeping guns out of the hands of those who, by current law, are not supposed to have them,” Cornyn said.

Rep. Veronica Escobar of Texas, a member of the House Judiciary Committee that advanced a gun bill last week, was among the Democrats who pushed back. In 2019, a man killed 23 people during an attack at a Walmart in her El Paso district.

“It’s not just schools. It’s the guns. This is a real opportunity for serious reform. Don’t give us a fig leaf,” Escobar tweeted.

Negotiations continue

Connecticut Democratic Sen. Christopher S. Murphy, the key negotiator for his party in the Senate, said at the event on the National Mall that “we’re not going to settle for a piece of legislation that just checks a box. We’re only going to move forward with a piece of legislation that saves lives.”

Speaker Nancy Pelosi said at the event that the House should still proceed with the bills in the face of Republican opposition, saying gun violence had claimed too many lives across the country.

“It is a message I send to elected officials all the time. You can’t vote for these bills because it is a problem for you politically?” Pelosi said. “Understand this, your political survival is nothing compared to the survival of our children.”

The House action follows a racially motivated attack in Buffalo, New York, that left 10 dead; an attack on an elementary school in Uvalde, Texas, that killed 19 children; and an attack at a medical facility in Oklahoma that killed another four people.

The White House announced Tuesday that Murphy would meet with President Joe Biden about the status of the Senate talks. And Majority Leader Charles E. Schumer said Senate Democrats would discuss them as well on Tuesday afternoon.

“We know that we’re not going to get everything we want, we know that the push for even more meaningful gun safety will continue after this debate, but making real progress is very important,” Schumer said in a floor speech.

Republicans have so far resisted efforts to expand background checks or restrict purchases of certain firearms.

House action

In the House, one bill rolls together eight individual measures, including language to increase the age to buy some rifles, limit magazine sizes, codify regulations banning bump stocks and ghost guns, and provide standards for safe gun storage.

Many Republicans are expected to oppose it. Rep. Jim Jordan of Ohio, the top Republican on the House Judiciary Committee, wrote that the bill “is a Democrat one-size-fits-all gun control bill that would place significant burdens on Americans’ Second Amendment rights while failing to meaningfully prevent gun violence or to improve public safety.”

Democrats had hoped to stir up some bipartisan support for that bill in particular, to the point that 21 moderates petitioned leadership for individual votes on parts of the package in a letter last week. The House Rules Committee may set up individual votes on parts of the broader bill as part of a vote series starting Wednesday.

Democrats have higher hopes for a bill from Rep. Lucy McBath, D-Ga., to establish a “red flag” procedure in federal courts, allowing individuals and police to seek extreme risk protection orders for the temporary seizure of firearms.